Sex-specific computational models of the spontaneously hypertensive rat kidneys: factors affecting nitric oxide bioavailability

Sex-specific computational models of the spontaneously hypertensive rat kidneys: factors affecting nitric oxide bioavailability. Am J Physiol Renal Physiol 313: F174 –F183, 2017. First published March 29, 2017; doi:10.1152/ajprenal.00482.2016.—The goals of this study were to 1) develop a computational model of solute transport and oxygenation in the kidney of the female spontaneously hypertensive rat (SHR), and 2) apply that model to investigate sex differences in nitric oxide (NO) levels in SHR and their effects on medullary oxygenation and oxidative stress. To accomplish these goals, we first measured NO synthase (NOS) 1 and NOS3 protein expression levels in total renal microvessels of male and female SHR. We found that the expression of both NOS1 and NOS3 is higher in the renal vasculature of females compared with males. To predict the implications of that finding on medullary oxygenation and oxidative stress levels, we developed a detailed computational model of the female SHR kidney. The model was based on a published male kidney model and represents solute transport and the biochemical reactions among O2, NO, and superoxide (O2 ) in the renal medulla. Model simulations conducted using both male and female SHR kidney models predicted significant radial gradients in interstitial fluid oxygen tension (PO2) and NO and O2 concentration in the outer medulla and upper inner medulla. The models also predicted that increases in endothelial NO-generating capacity, even when limited to specific vascular segments, may substantially raise medullary NO and PO2 levels. Other potential sex differences in SHR, including O2 production rate, are predicted to significantly impact oxidative stress levels, but effects on NO concentration and PO2 are limited.This research was supported by the National Institute of Diabetes and Digestive and Kidney Diseases Grant R01-DK-106102 to A. T. Layton, and by American Heart Association Grant 14GRNT20480199 to J. C. Sullivan. (R01-DK-106102 - National Institute of Diabetes and Digestive and Kidney Diseases; 14GRNT20480199 - American Heart Association)Accepted manuscrip

Recent advances in the modelling of renal function

Differential equation models have become an indispensable tool in the effort towards a complete understanding of hypertonic urine formation. Recent advances in this field include the treatment of a kidney model as an inverse prob lern, the modelling of the three-dimensional Organization of the renal medulla, and dynamic models for the tubuloglomerular feedback mechanism. The latter make use of techniques from bifurcation and chaos theory

Multiscale modelling of fluid and solute transport in soft tissues and microvessels

This study focuses on the movement of particles and extracellular fluid in soft tissues and microvessels. It analyzes modeling applications in biological and physiological fluids at a range of different length scales: from between a few tens to several hundred nanometers, on the endothelial glycocalyx and its effects on interactions between blood and the vessel wall; to a few micrometers, on movement of blood cells in capillaries and transcapillary exchange; to a few millimetres and centimetres, on extracellular matrix deformation and interstitial fluid movement in soft tissues. Interactions between blood cells and capillary wall are discussed when the sizes of the two are of the same order of magnitude, with the glycocalyx on the endothelial and red cell membranes being considered. Exchange of fluid, solutes, and gases by microvessels are highlighted when capillaries have counter-current arrangements. This anatomical feature exists in a number of tissues and is the key in the renal medulla on the urinary concentrating mechanism. The paper also addresses an important phenomenon on the transport of macromolecules. Concentration polarization of hyaluronan on the synovial lining of joint cavities is presented to demonstrate how the mechanism works in principle and how model predictions agree to experimental observations quantitatively

Mathematical Model of Ammonia Handling in the Rat Renal Medulla

The kidney is one of the main organs that produces ammonia and release it into the circulation. Under normal conditions, between 30 and 50% of the ammonia produced in the kidney is excreted in the urine, the rest being absorbed into the systemic circulation via the renal vein. In acidosis and in some pathological conditions, the proportion of urinary excretion can increase to 70% of the ammonia produced in the kidney. Mechanisms regulating the balance between urinary excretion and renal vein release are not fully understood. We developed a mathematical model that reflects current thinking about renal ammonia handling in order to investigate the role of each tubular segment and identify some of the components which might control this balance. The model treats the movements of water, sodium chloride, urea, NH3 and [Formula: see text], and non-reabsorbable solute in an idealized renal medulla of the rat at steady state. A parameter study was performed to identify the transport parameters and microenvironmental conditions that most affect the rate of urinary ammonia excretion. Our results suggest that urinary ammonia excretion is mainly determined by those parameters that affect ammonia recycling in the loops of Henle. In particular, our results suggest a critical role for interstitial pH in the outer medulla and for luminal pH along the inner medullary collecting ducts

Cell volume regulation in the proximal tubule of rat kidney proximal tubule cell volume regulation

We developed a dynamic model of a rat proximal convoluted tubule cell in order to investigate cell volume regulation mechanisms in this nephron segment. We examined whether regulatory volume decrease (RVD), which follows exposure to a hyposmotic peritubular solution, can be achieved solely via stimulation of basolateral K^+ and Cl^− channels and Na^+–HCO₃^− cotransporters. We also determined whether regulatory volume increase (RVI), which follows exposure to a hyperosmotic peritubular solution under certain conditions, may be accomplished by activating basolateral Na^+/H^+ exchangers. Model predictions were in good agreement with experimental observations in mouse proximal tubule cells assuming that a 10% increase in cell volume induces a fourfold increase in the expression of basolateral K+ and Cl− channels and Na+–HCO₃^− cotransporters. Our results also suggest that in response to a hyposmotic challenge and subsequent cell swelling, Na^+–HCO₃^− cotransporters are more efficient than basolateral K^+ and Cl^− channels at lowering intracellular osmolality and reducing cell volume. Moreover, both RVD and RVI are predicted to stabilize net transcellular Na^+ reabsorption, that is, to limit the net Na^+ flux decrease during a hyposmotic challenge or the net Na^+ flux increase during a hyperosmotic challenge.This research was supported by the National Institutes of Health, National Institute of Diabetes and Digestive and Kidney Diseases, via grant R01DK106102 to AT Layton. (R01DK106102 - National Institutes of Health, National Institute of Diabetes and Digestive and Kidney Diseases)Accepted manuscrip

A multiscale model for collagen alignment in wound healing

It is thought that collagen alignment plays a significant part in scar tissue formation during dermal wound healing. We present a multiscale model for collagen deposition and alignment during this process. We consider fibroblasts as discrete units moving within an extracellular matrix of collagen and fibrin modelled as continua. Our model includes flux induced alignment of collagen by fibroblasts, and contact guidance of fibroblasts by collagen fibres. We can use the model to predict the effects of certain manipulations, such as varying fibroblast speed, or placing an aligned piece of tissue in the wound. We also simulate experiments which alter the TGF-β concentrations in a healing dermal wound and use the model to offer an explanation of the observed influence of this growth factor on scarring

Cancer modelling: Getting to the heart of the problem

Paradoxically, improvements in healthcare that have enhanced the life expectancy of humans in the Western world have, indirectly, increased the prevalence of certain types of cancer such as prostate and breast. It remains unclear whether this phenomenon should be attributed to the ageing process itself or the cumulative effect of prolonged exposure to harmful environmental stimuli such as ultraviolet light, radiation and carcinogens (Franks and Teich, 1988). Equally, there is also compelling evidence that certain genetic abnormalities can predispose individuals to specific cancers (Ilyas et al., 1999). The variety of factors that have been implicated in the development of solid tumours stems, to a large extent, from the fact that ‘cancer’ is a generic term, often used to characterize a series of disorders that share common features. At this generic level of description, cancer may be viewed as a cellular disease in which controls that usually regulate growth and maintain homeostasis are disrupted. Cancer is typically initiated by genetic mutations that lead to enhanced mitosis of a cell lineage and the formation of an avascular tumour. Since it receives nutrients by diffusion from the surrounding tissue, the size of an avascular tumour is limited to several millimeters in diameter. Further growth relies on the tumour acquiring the ability to stimulate the ingrowth of a new, circulating blood supply from the host vasculature via a process termed angiogenesis (Folkman, 1974). Once vascularised, the tumour has access to a vast nutrient source and rapid growth ensues. Further, tumour fragments that break away from the primary tumour, on entering the vasculature, may be transported to other organs in which they may establish secondary tumours or metastases that further compromise the host. Invasion is another key feature of solid tumours whereby contact with the tissue stimulates the production of enzymes that digest the tissue, liberating space into which the tumour cells migrate. Thus, cancer is a complex, multiscale process. The spatial scales of interest range from the subcellular level, to the cellular and macroscopic (or tissue) levels while the timescales may vary from seconds (or less) for signal transduction pathways to months for tumour doubling times The variety of phenomena involved, the range of spatial and temporal scales over which they act and the complex way in which they are inter-related mean that the development of realistic theoretical models of solid tumour growth is extremely challenging. While there is now a large literature focused on modelling solid tumour growth (for a review, see, for example, Preziosi, 2003), existing models typically focus on a single spatial scale and, as a result, are unable to address the fundamental problem of how phenomena at different scales are coupled or to combine, in a systematic manner, data from the various scales. In this article, a theoretical framework will be presented that is capable of integrating a hierarchy of processes occurring at different scales into a detailed model of solid tumour growth (Alarcon et al., 2004). The model is formulated as a hybrid cellular automaton and contains interlinked elements that describe processes at each spatial scale: progress through the cell cycle and the production of proteins that stimulate angiogenesis are accounted for at the subcellular level; cell-cell interactions are treated at the cellular level; and, at the tissue scale, attention focuses on the vascular network whose structure adapts in response to blood flow and angiogenic factors produced at the subcellular level. Further coupling between the different spatial scales arises from the transport of blood-borne oxygen into the tissue and its uptake at the cellular level. Model simulations will be presented to illustrate the effect that spatial heterogeneity induced by blood flow through the vascular network has on the tumour’s growth dynamics and explain how the model may be used to compare the efficacy of different anti-cancer treatment protocols

Adaptive changes in GFR, tubular morphology, and transport in subtotal nephrectomized kidneys: modeling and analysis

Removal of renal mass stimulates anatomical and functional adaptations in the surviving nephrons, including elevations in single-nephron glomerular filtration rate (SNGFR) and tubular hypertrophy. A goal of this study is to assess the extent to which the concomitant increases in filtered load and tubular transport capacity preserve homeostasis of water and salt. To accomplish that goal, we developed computational models to simulate solute transport and metabolism along nephron populations in a uninephrectomized (UNX) rat and a 5/6-nephrectomized (5/6-NX) rat. Model simulations indicate that nephrectomy-induced SNGFR increase and tubular hypertrophy go a long way to normalize excretion, but alone are insufficient to fully maintain salt balance. We then identified increases in the protein density of Na+-K+-ATPase, Na+-K+-2Cl- cotransporter, Na+-Cl- cotransporter, and epithelial Na+ channel, such that the UNX and 5/6-NX models predict urine flow and urinary Na+ and K+ excretions that are similar to sham levels. The models predict that, in the UNX and 5/6-NX kidneys, fractional water and salt reabsorption is similar to sham along the initial nephron segments (i.e., from the proximal tubule to the distal convoluted tubule), with a need to further reduce Na+ reabsorption and increase K+ secretion primarily along the connecting tubules and collecting ducts to achieve balance. Additionally, the models predict that, given the substantially elevated filtered and thus transport load among each of the surviving nephrons, oxygen consumption per nephron segment in a UNX or 5/6-NX kidney increases substantially. But due to the reduced nephron population, whole animal renal oxygen consumption is lower. The efficiency of tubular Na+ transport in the UNX and 5/6-NX kidneys is predicted to be similar to sham.This research was supported by the Department of Veterans Affairs (to V. Vallon) and by the National Institutes of Health National Institute of Diabetes and Digestive and Kidney Diseases Grants R01-DK-56248 (to V. Vallon), R01-DK-106102 (A. T. Layton and V. Vallon), and the University of Alabama at Birmingham/ University of California San Diego O'Brien Center for Acute Kidney Injury Research NIH-P30-DK-079337 (to V. Vallon). (Department of Veterans Affairs; R01-DK-56248 - National Institutes of Health National Institute of Diabetes and Digestive and Kidney Diseases; R01-DK-106102 - National Institutes of Health National Institute of Diabetes and Digestive and Kidney Diseases; NIH-P30-DK-079337 - University of Alabama at Birmingham/ University of California San Diego O'Brien Center for Acute Kidney Injury Research)Accepted manuscrip

Glucose-induced down regulation of thiamine transporters in the kidney proximal tubular epithelium produces thiamine insufficiency in diabetes

Increased renal clearance of thiamine (vitamin B1) occurs in experimental and clinical diabetes producing thiamine insufficiency mediated by impaired tubular re-uptake and linked to the development of diabetic nephropathy. We studied the mechanism of impaired renal re-uptake of thiamine in diabetes. Expression of thiamine transporter proteins THTR-1 and THTR-2 in normal human kidney sections examined by immunohistochemistry showed intense polarised staining of the apical, luminal membranes in proximal tubules for THTR-1 and THTR-2 of the cortex and uniform, diffuse staining throughout cells of the collecting duct for THTR-1 and THTR-2 of the medulla. Human primary proximal tubule epithelial cells were incubated with low and high glucose concentration, 5 and 26 mmol/l, respectively. In high glucose concentration there was decreased expression of THTR-1 and THTR-2 (transporter mRNA: −76% and −53% respectively, p<0.001; transporter protein −77% and −83% respectively, p<0.05), concomitant with decreased expression of transcription factor specificity protein-1. High glucose concentration also produced a 37% decrease in apical to basolateral transport of thiamine transport across cell monolayers. Intensification of glycemic control corrected increased fractional excretion of thiamine in experimental diabetes. We conclude that glucose-induced decreased expression of thiamine transporters in the tubular epithelium may mediate renal mishandling of thiamine in diabetes. This is a novel mechanism of thiamine insufficiency linked to diabetic nephropathy

Renal potassium handling in rats with subtotal nephrectomy: modeling and analysis

We sought to decipher the mechanisms underlying the kidney's response to changes in K+ load and intake, under physiological and pathophysiological conditions. To accomplish that goal, we applied a published computational model of epithelial transport along rat nephrons in a sham rat, an uninephrectomized (UNX) rat, and a 5/6-nephrectomized (5/6-NX) rat that also considers adaptations in glomerular filtration rate and tubular growth. Model simulations of an acute K+ load indicate that elevated expression levels and activities of Na+/K+-ATPase, epithelial sodium channels, large-conductance Ca2+-activated K+ channels, and renal outer medullary K+ channels, together with downregulation of sodium-chloride cotransporters (NCC), increase K+ secretion along the connecting tubule, resulting in a >6-fold increase in urinary K+ excretion in sham rats, which substantially exceeds the filtered K+ load. In the UNX and 5/6-NX models, the acute K+ load is predicted to increase K+ excretion, but at significantly reduced levels compared with sham. Acute K+ load is accompanied by natriuresis in sham rats. Model simulations suggest that the lesser natriuretic effect observed in the nephrectomized groups may be explained by impaired NCC downregulation in these kidneys. At a single-nephron level, a high K+ intake raises K+ secretion along the connecting tubule and reabsorption along the collecting duct in sham, and even more in UNX and 5/6-NX. However, the increased K+ secretion per tubule fails to sufficiently compensate for the reduction in nephron number, such that nephrectomized rats have an impaired ability to excrete an acute or chronic K+ load.This research was supported by the Department of Veterans Affairs (V. Vallon), National Institute of Diabetes and Digestive and Kidney Diseases (NIDDK) Grants R01-DK-112042 (V. Vallon) and R01-DK-106102 (A. T. Layton and V. Vallon), and University of Alabama at Birmingham-University of California San Diego O'Brien Center for Acute Kidney Injury Research (NIDDK Grant P30-DK-079337; V. Vallon). (Department of Veterans Affairs; R01-DK-112042 - National Institute of Diabetes and Digestive and Kidney Diseases (NIDDK); R01-DK-106102 - National Institute of Diabetes and Digestive and Kidney Diseases (NIDDK); P30-DK-079337 - University of Alabama at Birmingham-University of California San Diego O'Brien Center for Acute Kidney Injury Research (NIDDK Grant))Accepted manuscrip